With blend4web 16.9.2, the scene used for "fast preview" appears to be chosen based on the scene's name. E.g, a scene named with "A" will always be previewed, even if the current scene in blender is a different scene called "B".

IMO this is pretty unintuitive. I expected it to use the currently active scene (bpy.context.scene). If it's important to be able to have fast preview consistently pick a specific scene, then I'd vote for having a separate option, something like "preview scene".